Valuation of flexible insurance contracts
Authors:
A. V. Melnikov, M. M. Moliboga and V. S. Skornyakova
Journal:
Theor. Probability and Math. Statist. 73 (2006), 109-115
MSC (2000):
Primary 60H30, 91B28, 91B30
DOI:
https://doi.org/10.1090/S0094-9000-07-00685-0
Published electronically:
January 17, 2007
MathSciNet review:
2213845
Full-text PDF Free Access
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Additional Information
Abstract: This work is devoted to the study of insurance contracts based on risky instruments of the financial market. In the case of Black and Scholes for constant and stochastic volatility, we present specific formulas for the valuation of premiums for contracts of pure endowment with guarantee.
References
- N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones, and C. I. Nesbitt, Actuarial Mathematics, Society of Actuaries, Schaumburg, Illinois, 1997.
- M. J. Brennan and E. S. Schwartz, The pricing of equity-linked life insurance policies with an asset value guarantee, Journal of Financial Economics 3 (1976), 195–213.
- K. Aase and S. Persson, Pricing of unit-linked insurance policies, Scandinavian Actuarial Journal 1 (1994), 26–52.
- P. P. Boyle and M. R. Hardy, Reserving for maturity guarantees: Two approaches, Insurance: Mathematics and Economics 21 (1997), 113–127.
- T. Møller, Risk-minimizing hedging strategies for unit-linked life-insurance contracts, Astin Bulletin 28 (1998), 17–47.
- Thomas Møller, Hedging equity-linked life insurance contracts, N. Am. Actuar. J. 5 (2001), no. 2, 79–95. MR 2012038, DOI https://doi.org/10.1080/10920277.2001.10595986
- A. V. Mel′nikov, S. N. Volkov, and M. L. Nechaev, Mathematics of financial obligations, Translations of Mathematical Monographs, vol. 212, American Mathematical Society, Providence, RI, 2002. Translated from the 2001 Russian original by H. H. McFaden. MR 1918716
- N. V. Krylov, Controlled diffusion processes, Applications of Mathematics, vol. 14, Springer-Verlag, New York-Berlin, 1980. Translated from the Russian by A. B. Aries. MR 601776
- V. S. Vladimirov, Uravneniya matematicheskoĭ fiziki, 4th ed., “Nauka”, Moscow, 1981 (Russian). MR 653331
- A. V. Melnikov and M. L. Nechaev, On the calculations of flexible life insurance contracts in Gaussian financial environment (2003) (to appear).
References
- N. L. Bowers, H. U. Gerber, J. C. Hickman, D. A. Jones, and C. I. Nesbitt, Actuarial Mathematics, Society of Actuaries, Schaumburg, Illinois, 1997.
- M. J. Brennan and E. S. Schwartz, The pricing of equity-linked life insurance policies with an asset value guarantee, Journal of Financial Economics 3 (1976), 195–213.
- K. Aase and S. Persson, Pricing of unit-linked insurance policies, Scandinavian Actuarial Journal 1 (1994), 26–52.
- P. P. Boyle and M. R. Hardy, Reserving for maturity guarantees: Two approaches, Insurance: Mathematics and Economics 21 (1997), 113–127.
- T. Møller, Risk-minimizing hedging strategies for unit-linked life-insurance contracts, Astin Bulletin 28 (1998), 17–47.
- T. Møller, Hedging equity-linked life insurance contracts, North American Actuarial Journal 5 (2001), no. 2, 79–95. MR 2012038
- A. V. Melnikov, S. N. Volkov, and M. L. Nechaev, Mathematics of Financial Obligations, AMS, Providence, RI, 2002. MR 1918716 (2003f:91055)
- N. V. Krylov, Controlled Diffusion Processes, Springer, 1980. MR 601776 (82a:60062)
- V. S. Vladimirov, Equations of Mathematical Physics, “Nauka”, Moscow, 1982. (Russian) MR 0653331 (83i:00029)
- A. V. Melnikov and M. L. Nechaev, On the calculations of flexible life insurance contracts in Gaussian financial environment (2003) (to appear).
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Additional Information
A. V. Melnikov
Affiliation:
Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Address at time of publication:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada
Email:
melnikov@ualberta.ca
M. M. Moliboga
Affiliation:
Efficient Capital Management, LLC, Naperville, Illinois
Email:
marat@efficientcapital.com
V. S. Skornyakova
Affiliation:
Mercer Investment Consulting, Montreal, Canada
Email:
vskorn@shaw.ca
Received by editor(s):
March 17, 2003
Published electronically:
January 17, 2007
Additional Notes:
The first author was supported in part by NSERC grant G121210913
Article copyright:
© Copyright 2007
American Mathematical Society
